This report contains different plots and tables that may be relevant for analysing the results. Observe:
alg1Given a problem consisting of \(m\)
subproblems with \(Y_N^s\) given for
each subproblem \(s\), we use a
filtering algorithm to find \(Y_N\)
(alg1).
The following instance/problem groups are generated given:
u and l. [4 options]1235/1280 problems have been solved, i.e. 45 remaining:
## [1] "alg1-prob-5-100|100|100|100|100-uuull-5_1.json"
## [2] "alg1-prob-5-100|100|100|100|100-uuull-5_2.json"
## [3] "alg1-prob-5-100|100|100|100|100-uuull-5_3.json"
## [4] "alg1-prob-5-100|100|100|100|100-uuull-5_4.json"
## [5] "alg1-prob-5-100|100|100|100|100-uuull-5_5.json"
## [6] "alg1-prob-5-200|200|200|200|200-mmmmm-5_1.json"
## [7] "alg1-prob-5-200|200|200|200|200-mmmmm-5_2.json"
## [8] "alg1-prob-5-200|200|200|200|200-mmmmm-5_3.json"
## [9] "alg1-prob-5-200|200|200|200|200-mmmmm-5_4.json"
## [10] "alg1-prob-5-200|200|200|200|200-mmmmm-5_5.json"
## [11] "alg1-prob-5-200|200|200|200|200-uuull-5_1.json"
## [12] "alg1-prob-5-200|200|200|200|200-uuull-5_2.json"
## [13] "alg1-prob-5-200|200|200|200|200-uuull-5_3.json"
## [14] "alg1-prob-5-200|200|200|200|200-uuull-5_4.json"
## [15] "alg1-prob-5-200|200|200|200|200-uuull-5_5.json"
## [16] "alg1-prob-5-200|200|200|200|200-uuuuu-5_1.json"
## [17] "alg1-prob-5-200|200|200|200|200-uuuuu-5_2.json"
## [18] "alg1-prob-5-200|200|200|200|200-uuuuu-5_3.json"
## [19] "alg1-prob-5-200|200|200|200|200-uuuuu-5_4.json"
## [20] "alg1-prob-5-200|200|200|200|200-uuuuu-5_5.json"
## [21] "alg1-prob-5-300|300|300|300|300-lllll-5_1.json"
## [22] "alg1-prob-5-300|300|300|300|300-lllll-5_2.json"
## [23] "alg1-prob-5-300|300|300|300|300-lllll-5_3.json"
## [24] "alg1-prob-5-300|300|300|300|300-lllll-5_4.json"
## [25] "alg1-prob-5-300|300|300|300|300-lllll-5_5.json"
## [26] "alg1-prob-5-300|300|300|300|300-mmmmm-5_1.json"
## [27] "alg1-prob-5-300|300|300|300|300-mmmmm-5_2.json"
## [28] "alg1-prob-5-300|300|300|300|300-mmmmm-5_3.json"
## [29] "alg1-prob-5-300|300|300|300|300-mmmmm-5_4.json"
## [30] "alg1-prob-5-300|300|300|300|300-mmmmm-5_5.json"
## [31] "alg1-prob-5-300|300|300|300|300-uuull-5_1.json"
## [32] "alg1-prob-5-300|300|300|300|300-uuull-5_2.json"
## [33] "alg1-prob-5-300|300|300|300|300-uuull-5_3.json"
## [34] "alg1-prob-5-300|300|300|300|300-uuull-5_4.json"
## [35] "alg1-prob-5-300|300|300|300|300-uuull-5_5.json"
## [36] "alg1-prob-5-300|300|300|300|300-uuuuu-5_1.json"
## [37] "alg1-prob-5-300|300|300|300|300-uuuuu-5_2.json"
## [38] "alg1-prob-5-300|300|300|300|300-uuuuu-5_3.json"
## [39] "alg1-prob-5-300|300|300|300|300-uuuuu-5_4.json"
## [40] "alg1-prob-5-300|300|300|300|300-uuuuu-5_5.json"
## [41] "alg1-prob-5-50|50|50|50|50-uuull-5_1.json"
## [42] "alg1-prob-5-50|50|50|50|50-uuull-5_2.json"
## [43] "alg1-prob-5-50|50|50|50|50-uuull-5_3.json"
## [44] "alg1-prob-5-50|50|50|50|50-uuull-5_4.json"
## [45] "alg1-prob-5-50|50|50|50|50-uuull-5_5.json"
1235/1235 problems have 5 instances solved for each configuration. Configurations with lees that 5 solved:
## # A tibble: 9 × 5
## # Groups: p, m, method [4]
## p m method spAveCard solved
## <dbl> <dbl> <chr> <dbl> <int>
## 1 5 5 l 300 0
## 2 5 5 m 200 0
## 3 5 5 m 300 0
## 4 5 5 u 200 0
## 5 5 5 u 300 0
## 6 5 5 ul 50 0
## 7 5 5 ul 100 0
## 8 5 5 ul 200 0
## 9 5 5 ul 300 0
73/1235 have not been classified at all:
## [1] "alg1-prob-4-200|200|200|200|200-mmmmm-5_1.json"
## [2] "alg1-prob-4-200|200|200|200|200-mmmmm-5_2.json"
## [3] "alg1-prob-4-200|200|200|200|200-mmmmm-5_3.json"
## [4] "alg1-prob-4-300|300|300|300|300-lllll-5_4.json"
## [5] "alg1-prob-4-300|300|300|300|300-mmmmm-5_1.json"
## [6] "alg1-prob-4-300|300|300|300|300-mmmmm-5_2.json"
## [7] "alg1-prob-4-300|300|300|300|300-mmmmm-5_3.json"
## [8] "alg1-prob-4-300|300|300|300|300-mmmmm-5_4.json"
## [9] "alg1-prob-4-300|300|300|300|300-mmmmm-5_5.json"
## [10] "alg1-prob-4-300|300|300|300|300-uuull-5_2.json"
## [11] "alg1-prob-4-300|300|300|300|300-uuull-5_3.json"
## [12] "alg1-prob-4-300|300|300|300|300-uuull-5_4.json"
## [13] "alg1-prob-4-300|300|300|300|300-uuull-5_5.json"
## [14] "alg1-prob-4-300|300|300|300|300-uuuuu-5_2.json"
## [15] "alg1-prob-4-300|300|300|300|300-uuuuu-5_3.json"
## [16] "alg1-prob-4-300|300|300|300|300-uuuuu-5_4.json"
## [17] "alg1-prob-4-300|300|300|300|300-uuuuu-5_5.json"
## [18] "alg1-prob-4-50|50|50|50|50-lllll-5_1.json"
## [19] "alg1-prob-4-50|50|50|50|50-lllll-5_2.json"
## [20] "alg1-prob-4-50|50|50|50|50-lllll-5_3.json"
## [21] "alg1-prob-4-50|50|50|50|50-lllll-5_4.json"
## [22] "alg1-prob-4-50|50|50|50|50-lllll-5_5.json"
## [23] "alg1-prob-5-100|100-uu-2_2.json"
## [24] "alg1-prob-5-100|100-uu-2_3.json"
## [25] "alg1-prob-5-100|100|100|100|100-lllll-5_1.json"
## [26] "alg1-prob-5-100|100|100|100|100-lllll-5_2.json"
## [27] "alg1-prob-5-100|100|100|100|100-lllll-5_3.json"
## [28] "alg1-prob-5-100|100|100|100|100-lllll-5_4.json"
## [29] "alg1-prob-5-100|100|100|100|100-lllll-5_5.json"
## [30] "alg1-prob-5-100|100|100|100|100-mmmmm-5_5.json"
## [31] "alg1-prob-5-100|100|100|100|100-uuuuu-5_1.json"
## [32] "alg1-prob-5-100|100|100|100|100-uuuuu-5_4.json"
## [33] "alg1-prob-5-100|100|100|100|100-uuuuu-5_5.json"
## [34] "alg1-prob-5-200|200|200|200-llll-4_1.json"
## [35] "alg1-prob-5-200|200|200|200-llll-4_2.json"
## [36] "alg1-prob-5-200|200|200|200-llll-4_3.json"
## [37] "alg1-prob-5-200|200|200|200-llll-4_4.json"
## [38] "alg1-prob-5-200|200|200|200-llll-4_5.json"
## [39] "alg1-prob-5-200|200|200|200-mmmm-4_1.json"
## [40] "alg1-prob-5-200|200|200|200-mmmm-4_2.json"
## [41] "alg1-prob-5-200|200|200|200-mmmm-4_3.json"
## [42] "alg1-prob-5-200|200|200|200-mmmm-4_4.json"
## [43] "alg1-prob-5-200|200|200|200-mmmm-4_5.json"
## [44] "alg1-prob-5-200|200|200|200-uull-4_1.json"
## [45] "alg1-prob-5-200|200|200|200-uull-4_2.json"
## [46] "alg1-prob-5-200|200|200|200-uull-4_3.json"
## [47] "alg1-prob-5-200|200|200|200-uull-4_4.json"
## [48] "alg1-prob-5-200|200|200|200-uull-4_5.json"
## [49] "alg1-prob-5-200|200|200|200|200-lllll-5_1.json"
## [50] "alg1-prob-5-200|200|200|200|200-lllll-5_2.json"
## [51] "alg1-prob-5-200|200|200|200|200-lllll-5_3.json"
## [52] "alg1-prob-5-200|200|200|200|200-lllll-5_4.json"
## [53] "alg1-prob-5-200|200|200|200|200-lllll-5_5.json"
## [54] "alg1-prob-5-300|300|300|300-llll-4_1.json"
## [55] "alg1-prob-5-300|300|300|300-llll-4_2.json"
## [56] "alg1-prob-5-300|300|300|300-llll-4_3.json"
## [57] "alg1-prob-5-300|300|300|300-llll-4_4.json"
## [58] "alg1-prob-5-300|300|300|300-llll-4_5.json"
## [59] "alg1-prob-5-300|300|300|300-mmmm-4_1.json"
## [60] "alg1-prob-5-300|300|300|300-mmmm-4_2.json"
## [61] "alg1-prob-5-300|300|300|300-mmmm-4_3.json"
## [62] "alg1-prob-5-300|300|300|300-mmmm-4_4.json"
## [63] "alg1-prob-5-300|300|300|300-mmmm-4_5.json"
## [64] "alg1-prob-5-300|300|300|300-uull-4_1.json"
## [65] "alg1-prob-5-300|300|300|300-uull-4_2.json"
## [66] "alg1-prob-5-300|300|300|300-uull-4_3.json"
## [67] "alg1-prob-5-300|300|300|300-uull-4_4.json"
## [68] "alg1-prob-5-300|300|300|300-uull-4_5.json"
## [69] "alg1-prob-5-50|50|50|50|50-lllll-5_1.json"
## [70] "alg1-prob-5-50|50|50|50|50-lllll-5_2.json"
## [71] "alg1-prob-5-50|50|50|50|50-lllll-5_3.json"
## [72] "alg1-prob-5-50|50|50|50|50-lllll-5_4.json"
## [73] "alg1-prob-5-50|50|50|50|50-lllll-5_5.json"
463/1162 classified files have not been fully classified (only classified extreme).
Note that the width of objective \(i = 1, \ldots p\), \(w_i = [l_i, u_i]\) should be approx. \(10000m\). Check:
## # A tibble: 4 × 6
## m mean_width1 mean_width2 mean_width3 mean_width4 mean_width5
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 19245. 19221. 19213. 18996. 18690.
## 2 3 28760. 28800. 28689. 28479. 27847.
## 3 4 38302. 38348. 38158. 37758. 36803.
## 4 5 47840. 47994. 47848. 47431 44509.
What is \(|Y_N|\) given the different methods of generating the set of nondominated points for the subproblems?
## # A tibble: 4 × 3
## method mean_card n
## <chr> <dbl> <int>
## 1 l 1506031. 315
## 2 m 572395. 310
## 3 u 109824. 310
## 4 ul 206763. 300
Does \(p\) have an effect?
## # A tibble: 16 × 4
## # Groups: method [4]
## method p mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 8293. 80
## 2 m 2 6828. 80
## 3 u 2 1164. 80
## 4 ul 2 2920. 80
## 5 l 3 148913. 80
## 6 m 3 180435. 80
## 7 u 3 12475. 80
## 8 ul 3 26863. 80
## 9 l 4 1286899. 80
## 10 m 4 1063823. 80
## 11 u 4 110045. 80
## 12 ul 4 267769. 80
## 13 l 5 4784950. 75
## 14 m 5 1105081. 70
## 15 u 5 345012. 70
## 16 ul 5 637081. 60
Does \(m\) have an effect?
## # A tibble: 16 × 4
## # Groups: method [4]
## method m mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 8173. 80
## 2 m 2 5688. 80
## 3 u 2 4201. 80
## 4 ul 2 4923. 80
## 5 l 3 166384. 80
## 6 m 3 90077. 80
## 7 u 3 37283. 80
## 8 ul 3 90425. 80
## 9 l 4 1596091. 80
## 10 m 4 874692. 80
## 11 u 4 190675. 80
## 12 ul 4 485509. 80
## 13 l 5 4436637. 75
## 14 m 5 1425800. 70
## 15 u 5 221040. 70
## 16 ul 5 259341. 60
Let us try to fit the results using function \(y=c_1 s^{(c_2p)} m^{c_3p}\) (different functions was tried and this gave the highest \(R^2\)) for each method.
## # A tibble: 4 × 15
## method fit tidied r.squared adj.r.squared sigma statistic p.value df
## <chr> <list> <list> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 l <lm> <tibble> 0.856 0.855 1.05 929. 3.90e-132 2
## 2 m <lm> <tibble> 0.768 0.766 1.25 507. 5.07e- 98 2
## 3 ul <lm> <tibble> 0.903 0.903 0.747 1389. 1.89e-151 2
## 4 u <lm> <tibble> 0.947 0.947 0.527 2759. 6.52e-197 2
## # ℹ 6 more variables: logLik <dbl>, AIC <dbl>, BIC <dbl>, deviance <dbl>,
## # df.residual <int>, nobs <int>
## # A tibble: 4 × 4
## method c1 c2 c3
## <chr> <dbl> <dbl> <dbl>
## 1 l 83.0 0.0836 1.24
## 2 m 89.2 0.0847 1.11
## 3 ul 30.1 0.117 1.12
## 4 u 23.5 0.135 0.955
We classify the nondominated points into, extreme, supported non-extreme and unsupported.
## # A tibble: 1 × 3
## minPctEx avePctExt maxPctEx
## <dbl> <dbl> <dbl>
## 1 0.000461 0.0449 0.330
## # A tibble: 4 × 4
## method minPctEx avePctExt maxPctEx
## <chr> <dbl> <dbl> <dbl>
## 1 l 0.00443 0.0761 0.302
## 2 ul 0.00635 0.0719 0.330
## 3 m 0.000461 0.0205 0.147
## 4 u 0.00196 0.0132 0.104